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C7×A4×C25 #14523552

order2100
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productC7×A4×C25
unambiguous semidirect productC22⋊(C3×C7×C25)
unambiguous semidirect product(C22×C25)⋊(C3×C7)

Splittings

Fitting, HallC22×C7×C25 ⋊ C3
derived, SylowC22 ⋊ C3×C7×C25
HallC22×C25 ⋊ C3×C7
HallC22×C7 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25A4
commutator, hypocenterC22C3×C7×C25
FrattiniC5C5×C7×A4
FittingC22×C7×C25C3
socleC22×C5×C7C3×C5
prime radicalC5×C7×A4C5
cosocleC22×C5C3×C5×C7
LCSG ▷ C22
UCSC1 ◁ C7×C25

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 700

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofA4×C25×C49, C72×A4×C25, C7×C25×C22⋊ΓL(1,𝔽8), …
maximal normal subgroup ofA4×C25×C49, C72×A4×C25, C7×C11×A4×C25, …
maximal quotient ofA4×C25×C49, C72×A4×C25, C7×C25×C22⋊ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 32);