Finite Group Databasebeta

Q32×Dic23 #15675256

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

Aliases

direct productQ32×Dic23

Splittings

SylowC23 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC22D8×D23
commutatorC8×C23C22×C4
FrattiniC2×C8C22×D23
FittingC2×C23×Q32C2
socle, prime radicalC22×C23C2×D8
cosocleC2×C8×C23C23
hypercenterC2×Q32D23
hypocenterC23C4×Q32
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6369);