Finite Group Databasebeta

← Prev (#28587293) Next (#28587295) →

C8×#14273692 #28587294

order15104
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#14273692

Splittings

SylowC59 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC2×C59C22×C4×C8
FrattiniC22×C4C23×D59
FittingC8×C4⋊C4×C59C2
socle, prime radicalC23×C59C23×C4
cosocleC22×C4×C59C24
hypercenterC8×C4⋊C4D59
hypocenterC59C4×C8×Q8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 168173);