Finite Group Databasebeta

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C11×C11⋊C5×A5 #49137836

order36300
automorphism?
homologyAbelianization (H1) = C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C11⋊C5×A5
unambiguous semidirect productC11⋊(C5×C11×A5)
unambiguous semidirect product(C11×A5)⋊(C5×C11)

Splittings

Fitting, SylowC112 ⋊ C5×A5
socleC112×A5 ⋊ C5
derivedC11×A5 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC11C11⋊C5×A5
commutator, hypocenterC11×A5C5×C11
FrattiniC1G
FittingC112C5×A5
socleC112×A5C5
cosocleC11C5×C11×A5
LCSG ▷ C11×A5
UCSC1 ◁ C11

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 275

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,4,6,3)(5,8,9,11,7)(23,24,27,25,26);(1,3,4,7,6,10,8,2,5,9,11)(12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 972);