Finite Group Databasebeta

C2×C4×Q8×D109 #28376205

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

Aliases

direct productC2×C4×Q8×D109

Splittings

FittingC2×C4×Q8×C109 ⋊ C2
SylowC109 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC2×C4×Q8×C109C2
socleC23×C109C24
prime radicalC23×D109C23
cosocleC22×C109C25
hypercenterC2×C4×Q8D109
hypocenterC109C22×C4×Q8
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

1664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

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, 17683);