Finite Group Databasebeta

C2×#13092254 #15675697

order2944
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13092254

Splittings

FittingC2×C23×Q32 ⋊ C2
SylowC23 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#10625008
commutator, cosocleC16×C23C23
FrattiniC16C22×D23
FittingC2×C23×Q32C2
socleC22×C23D16
prime radicalC2×D368C2
hypercenterC2×Q32D23
hypocenterC23C2×SD64
LCSG ▷ C16×C23 ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6810);