Finite Group Databasebeta

D23×#405 #15681807

order2944
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productD23×#405

Splittings

FittingC23×#405 ⋊ C2
SylowC23 ⋊ C2×#405

Subgroups

subgroupG/H
centerC2×C8C22×D23
commutatorC2×C23C22×C42
FrattiniC2×C4C23×D23
FittingC23×#405C2
socleC22×C23C23×C4
prime radicalC23×D23C2×C4
cosocleC2×C4×C23C24
hypercenter#405D23
hypocenterC23C2×#405
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C8 ◁ #405

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

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, 12920);