Finite Group Databasebeta

Q32×D379 #37565670

order24256
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D379

Splittings

FittingQ32×C379 ⋊ C2
SylowC379 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D379
commutator, cosocleC8×C379C23
FrattiniC8C22×D379
FittingQ32×C379C2
socleC2×C379C2×D8
prime radicalC2×D379D8
hypercenterQ32D379
hypocenterC379C2×Q32
LCSG ▷ C8×C379 ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12128

Conjugacy classes & character table

2101 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 975);