Finite Group Databasebeta

C22×Q8×Dic107 #28349637

order13696
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×Dic107

Splittings

SylowC107 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC24C22×D107
commutatorC2×C107C24×C4
FrattiniC22C24×D107
FittingC23×Q8×C107C2
socle, prime radicalC24×C107C23
cosocleC22×C107C25
hypercenterC23×Q8D107
hypocenterC107C22×C4×Q8
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C24 ◁ C23×Q8

1664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 17686);