Finite Group Databasebeta

C23×C4×Dic118 #29495258

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC23×C4×Dic118

Splittings

SylowC59 ⋊ C23×C4×Q8

Subgroups

subgroupG/H
centerC24×C4C2×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
FittingC23×C42×C59C2
socle, prime radicalC25×C59C23
cosocleC22×C59C26
hypercenterC23×C42D59
hypocenterC59C23×C4×Q8
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C24×C4 ◁ C23×C42

12446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076137);