Finite Group Databasebeta

C23×Q8×D109 #28377826

order13952
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC23×Q8×D109

Splittings

FittingC23×Q8×C109 ⋊ C2
SylowC109 ⋊ C24×Q8

Subgroups

subgroupG/H
centerC24C22×D109
commutator, cosocleC2×C109C26
FrattiniC2C25×D109
FittingC23×Q8×C109C2
socleC24×C109C23
prime radicalC24×D109C22
hypercenterC23×Q8D109
hypocenterC109C24×Q8
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C23×Q8

6264 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, 19304);