Finite Group Databasebeta

D4×Dic23⋊C4 #15676294

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

Aliases

direct productD4×Dic23⋊C4

Splittings

SylowC23 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC2×C4×D4×C23C2
socle, cosocleC23×C23C24
prime radicalC22×D4×C23C22
hypercenterC2×C4×D4D23
hypocenterC23D4×C4⋊C4
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C4×D4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7407);