Finite Group Databasebeta

D59×#1381 #28503574

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD59×#1381

Splittings

FittingC59×#1381 ⋊ C2
SylowC59 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC2×C4D8×D59
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC59×#1381C2
socleC22×C59C2×#107
prime radicalC23×D59Q16
cosocleC22×C8×C59C23
hypercenter#1381D59
hypocenterC59C2×#1381
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84453);