Finite Group Databasebeta

D59×#1833 #28588858

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD59×#1833

Splittings

FittingC59×#1833 ⋊ C2
SylowC59 ⋊ C2×#1833

Subgroups

subgroupG/H
centerC4#117×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1833C2
socleC2×C59C2×#382
prime radicalC23×D59#41
cosocleC22×C4×C59C24
hypercenter#1833D59
hypocenterC59C2×#1833
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ #117 ◁ #1833

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 169737);