Finite Group Databasebeta

C2×D4×C23⋊C8 #15682070

order2944
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×C23⋊C8

Splittings

SylowC23 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D23
commutatorC2×C23C23×C8
FrattiniC2×C4C23×D23
FittingC2×C4×D4×C23C2
socleC23×C23C22×C4
prime radicalC22×D4×C23C4
cosocleC2×C4×C23C24
hypercenterC2×C4×D4D23
hypocenterC23C2×C8×D4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

616 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, 13183);