Finite Group Databasebeta

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C11×A4×C25 #15693111

order3300
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC11×A4×C25
unambiguous semidirect productC22⋊(C3×C11×C25)
unambiguous semidirect product(C22×C25)⋊(C3×C11)
unambiguous semidirect product(C22×C11×C25)⋊C3

Splittings

Fitting, HallC22×C11×C25 ⋊ C3
derived, SylowC22 ⋊ C3×C11×C25
HallC22×C25 ⋊ C3×C11
HallC22×C11 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25A4
commutator, hypocenterC22C3×C11×C25
FrattiniC5C5×C11×A4
FittingC22×C11×C25C3
socleC22×C5×C11C3×C5
prime radicalC5×C11×A4C5
cosocleC22×C5C3×C5×C11
LCSG ▷ C22
UCSC1 ◁ C11×C25

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 1100

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(12,13,14)

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×A4×C25, C11×C25×C22⋊ΓL(1,𝔽8), A4×C25×C121, …
maximal normal subgroup ofC7×C11×A4×C25, A4×C25×C121, C112×A4×C25
maximal quotient ofC7×C11×A4×C25, C11×C25×C22⋊ΓL(1,𝔽8), A4×C25×C121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 31);