Finite Group Databasebeta

C4×#10625160 #15686604

order2944
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#10625160

Splittings

FittingC4×#41×C23 ⋊ C2
SylowC23 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C23×D23
commutatorC2×C23C24×C4
FrattiniC22C24×D23
FittingC4×#41×C23C2
socle, cosocleC22×C23C25
prime radicalC2×#10625160C2
hypercenterC4×#41D23
hypocenterC23C4×H(5,𝔽2)
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C4×#41

1660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17717);