Finite Group Databasebeta

C4×Q32×D59 #28741960

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

Aliases

direct productC4×Q32×D59

Splittings

FittingC4×Q32×C59 ⋊ C2
SylowC59 ⋊ C2×C4×Q32

Subgroups

subgroupG/H
centerC2×C4D8×D59
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
FittingC4×Q32×C59C2
socleC22×C59C22×D8
prime radicalC22×D59C2×D8
cosocleC2×C8×C59C24
hypercenterC4×Q32D59
hypocenterC59C2×C4×Q32
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×Q32

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 322839);