Finite Group Databasebeta

C4×#16812635 #28362934

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16812635

Splittings

SylowC109 ⋊ C4×#108

Subgroups

subgroupG/H
centerC42D436
commutatorC4×C109C2×C42
FrattiniC22×C4C22×D109
FittingC2×C4×C8×C109C2
socleC22×C109C2×C4⋊C4
prime radicalC23×C109C2×Q8
cosocleC22×C4×C109C23
hypercenterC2×C4×C8D109
hypocenterC109C4×#108
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 4412);