Finite Group Databasebeta

C22×C22⋊Q8×D59 #29495328

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×C22⋊Q8×D59

Splittings

FittingC22×C22⋊Q8×C59 ⋊ C2
SylowC59 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC22×C22⋊Q8×C59C2
socleC24×C59C24
prime radicalC25×D59C22
hypercenterC22×C22⋊Q8D59
hypocenterC59C23×C22⋊Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

14078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076207);