Finite Group Databasebeta

C8×#67290 #15682352

order2944
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#67290

Splittings

FittingC8×D4×C23 ⋊ C2
SylowC23 ⋊ C8×#41

Subgroups

subgroupG/H
centerC2×C8C22×D23
commutatorC2×C23C23×C8
FrattiniC2×C4C23×D23
FittingC8×D4×C23C2
socleC22×C23C23×C4
prime radicalC2×#67290C4
cosocleC2×C4×C23C24
hypercenterC8×D4D23
hypocenterC23C8×#41
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C8 ◁ C8×D4

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13465);