Finite Group Databasebeta

C4×#10625118 #15675943

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#10625118

Splittings

FittingC2×C4×Q8×C23 ⋊ C2
SylowC23 ⋊ C4×#124

Subgroups

subgroupG/H
centerC22×C4C22×D23
commutatorC22×C23C23×C4
FrattiniC23C23×D23
FittingC2×C4×Q8×C23C2
socle, cosocleC23×C23C24
prime radicalC22×D92C22
hypercenterC2×C4×Q8D23
hypocenterC23C4×#124
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7056);