Finite Group Databasebeta

D59×#2108 #28741321

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

Aliases

direct productD59×#2108

Splittings

FittingC59×#2108 ⋊ C2
SylowC59 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC2×C16C22×D59
commutatorC2×C59C22×C4×C8
FrattiniC2×C8C23×D59
FittingC59×#2108C2
socleC22×C59C23×C8
prime radicalC23×D59C2×C8
cosocleC2×C8×C59C24
hypercenter#2108D59
hypocenterC59C2×#2108
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C16 ◁ #2108

854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 322200);