Finite Group Databasebeta

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C31×Dic23⋊C11 #44535874

order31372
automorphism?
homologyAbelianization (H1) = C4×C11×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×Dic23⋊C11
unambiguous semidirect productDic23⋊(C11×C31)
unambiguous semidirect product(C23⋊C11)⋊(C4×C31)
unambiguous semidirect product(C31×Dic23)⋊C11

Splittings

derived, SylowC23 ⋊ C4×C11×C31
HallC31×C23⋊C11 ⋊ C4
HallC31×Dic23 ⋊ C11
HallC23×C31 ⋊ C4×C11
HallC23⋊C11 ⋊ C4×C31
HallDic23 ⋊ C11×C31

Subgroups

subgroupG/H
center, hypercenterC2×C31AGL(1,𝔽23)
commutator, hypocenterC23C4×C11×C31
FrattiniC2C31×AGL(1,𝔽23)
Fitting, socleC2×C23×C31C2×C11
prime radicalC2×C31×C23⋊C11C2
cosocleC2×C23C2×C11×C31
LCSG ▷ C23
UCSC1 ◁ C2×C31

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2852

Conjugacy classes & character table

1426 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31372, 11);