Finite Group Databasebeta

C4×D8×D23 #15682144

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×D8×D23

Splittings

FittingC4×D8×C23 ⋊ C2
SylowC23 ⋊ C2×C4×D8

Subgroups

subgroupG/H
centerC2×C4D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC4×D8×C23C2
socleC22×C23C22×D4
prime radicalC2×D8×D23C2
cosocleC2×C4×C23C24
hypercenterC4×D8D23
hypocenterC23C2×C4×D8
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13257);