Finite Group Databasebeta

#104×Dic118 #28605386

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#104×Dic118

Splittings

SylowC59 ⋊ Q8×#104

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×#104×C59C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#41×C59C23
cosocleC22×C4×C59C24
hypercenterC4×#104D59
hypocenterC59Q8×#104
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 186265);