Finite Group Databasebeta

C22×Q8×Dic109 #28376208

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×Dic109

Splittings

SylowC109 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC24C22×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC23×Q8×C109C2
socle, prime radicalC24×C109C23
cosocleC22×C109C25
hypercenterC23×Q8D109
hypocenterC109C22×C4×Q8
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C23×Q8

1664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17686);