Finite Group Databasebeta

C8×#14273642 #28479230

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC8×#14273642

Splittings

SylowC59 ⋊ C8×#99

Subgroups

subgroupG/H
centerC2×C8C22⋊Dic59
commutatorC22×C59C2×C4×C8
FrattiniC23×C4C22×D59
FittingC2×C8×D4×C59C2
socleC22×C59C4×C22⋊C4
prime radicalC22×D4×C59C2×C4
cosocleC23×C4×C59C23
hypercenterC2×C8×D4D59
hypocenterC59C8×#99
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C2×C8×D4

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 60109);