Finite Group Databasebeta

C8×#14273643 #28479248

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×#14273643

Splittings

FittingC8×M16×C59 ⋊ C2
SylowC59 ⋊ C8×#100

Subgroups

subgroupG/H
centerC2×C8(C2×D59)⋊C4
commutatorC22×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC8×M16×C59C2
socleC22×C59C4×C22⋊C4
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenterC8×M16D59
hypocenterC59C8×#100
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C8×M16

542 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, 60127);