Finite Group Databasebeta

← Prev (#37536064) Next (#37536066) →

C4×#19153776 #37536065

order23168
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#19153776

Splittings

FittingC4×C22⋊C4×C181 ⋊ C2
SylowC181 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D181
commutatorC2×C181C22×C42
FrattiniC23C23×D181
FittingC4×C22⋊C4×C181C2
socle, cosocleC23×C181C24
prime radicalC22×C22⋊D181C22
hypercenterC4×C22⋊C4D181
hypocenterC181C42×D4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11584

Conjugacy classes & character table

3680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 6854);