Finite Group Databasebeta

D4×#14273649 #28604096

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×#14273649

Splittings

FittingC2×C8×D4×C59 ⋊ C2
SylowC59 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C8×D4×C59C2
socleC23×C59C22×D4
prime radicalC2×D4×D236C2
cosocleC22×C4×C59C24
hypercenterC2×C8×D4D59
hypocenterC59D4×#102
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 184975);