Finite Group Databasebeta

C22⋊Q8×C59⋊C8 #28596104

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22⋊Q8×C59⋊C8

Splittings

SylowC59 ⋊ C8×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D59
commutatorC22×C59C23×C8
FittingC4×C22⋊Q8×C59C2
socleC23×C59C23×C4
prime radicalC24×C59C22×C4
cosocleC22×C4×C59C24
hypercenterC4×C22⋊Q8D59
hypocenterC59C8×C22⋊Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 176983);