Finite Group Databasebeta

Q32×D383 #37588777

order24512
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D383

Splittings

FittingQ32×C383 ⋊ C2
SylowC383 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D383
commutator, cosocleC8×C383C23
FrattiniC8C22×D383
FittingQ32×C383C2
socleC2×C383C2×D8
prime radicalC2×D383D8
hypercenterQ32D383
hypocenterC383C2×Q32
LCSG ▷ C8×C383 ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12256

Conjugacy classes & character table

2123 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 975);