Finite Group Databasebeta

C22×Q8×Dic118 #29495756

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×Q8×Dic118

Splittings

SylowC59 ⋊ C22×Q82

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC22×C4×Q8×C59C2
socle, prime radicalC24×C59C24
hypercenterC22×C4×Q8D59
hypocenterC59C22×Q82
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C4×Q8

7846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076635);