Finite Group Databasebeta

D4×#14273663 #28606942

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD4×#14273663

Splittings

SylowC59 ⋊ D4×#108

Subgroups

subgroupG/H
centerC2×C4C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C8×D4×C59C2
socleC22×C59C22×C4⋊C4
prime radicalC22×D4×C59Q8
cosocleC22×C4×C59C24
hypercenterC2×C8×D4D59
hypocenterC59D4×#108
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C2×C8×D4

894 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, 187821);