Finite Group Databasebeta

#367×Dic59 #28504094

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#367×Dic59

Splittings

SylowC59 ⋊ C4×#367

Subgroups

subgroupG/H
centerC23D8×D59
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC2×C59×#367C2
socle, prime radicalC23×C59C2×D8
cosocleC22×C8×C59C23
hypercenterC2×#367D59
hypocenterC59C4×#367
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

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, 84973);