Finite Group Databasebeta

#368×Dic59 #28504103

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct product#368×Dic59

Splittings

SylowC59 ⋊ C4×#368

Subgroups

subgroupG/H
centerC2×C4D8×D59
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC2×C59×#368C2
socleC22×C59C2×#107
prime radicalC23×C59C2×Q16
cosocleC22×C8×C59C23
hypercenterC2×#368D59
hypocenterC59C4×#368
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#368

314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 84982);