Finite Group Databasebeta

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C4×#19153796 #37536258

order23168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#19153796

Splittings

FittingC4×C4⋊C4×C181 ⋊ C2
SylowC181 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D181
commutatorC22×C181C23×C4
FrattiniC23C23×D181
FittingC4×C4⋊C4×C181C2
socle, cosocleC23×C181C24
prime radicalC23×D181C23
hypercenterC4×C4⋊C4D181
hypocenterC181C4×C22⋊Q8
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11584

Conjugacy classes & character table

3656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 7047);