Finite Group Databasebeta

C4×C22⋊Q8×D59 #28747131

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×C22⋊Q8×D59

Splittings

FittingC4×C22⋊Q8×C59 ⋊ C2
SylowC59 ⋊ C2×C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC4×C22⋊Q8×C59C2
socle, cosocleC23×C59C25
prime radicalC24×D59C23
hypercenterC4×C22⋊Q8D59
hypocenterC59C2×C4×C22⋊Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

3854 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, 328010);