Finite Group Databasebeta

C2×Q32×Dic59 #28741964

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q32×Dic59

Splittings

SylowC59 ⋊ C2×C4×Q32

Subgroups

subgroupG/H
centerC23D8×D59
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
FittingC22×Q32×C59C2
socle, prime radicalC23×C59C2×D8
cosocleC2×C8×C59C24
hypercenterC22×Q32D59
hypocenterC59C2×C4×Q32
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322843);