Finite Group Databasebeta

D23×#322 #15671671

order2944
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productD23×#322

Splittings

FittingC23×#322 ⋊ C2
SylowC23 ⋊ C2×#322

Subgroups

subgroupG/H
center, FrattiniC42C22×D23
commutatorC2×C23C2×C4×C8
FittingC23×#322C2
socleC22×C23C2×C42
prime radicalC22×D23C42
cosocleC42×C23C23
hypercenter#322D23
hypocenterC23C2×#322
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C42 ◁ #322

248 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, 2784);