Finite Group Databasebeta

D4×#14273647 #28604089

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

Aliases

direct productD4×#14273647

Splittings

FittingD4×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingD4×C4⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC2×D4×D236C2
cosocleC22×C4×C59C24
hypercenterD4×C4⋊C4D59
hypocenterC59D4×#102
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 184968);