Finite Group Databasebeta

C4×Dic872 #28364892

order13952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic872

Splittings

SylowC109 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC2×C4D872
commutatorC8×C109C22×C4
FrattiniC2×C8C22×D109
FittingC4×C16×C109C2
socle, prime radicalC22×C109C2×D8
cosocleC2×C8×C109C23
hypercenterC4×C16D109
hypocenterC109C4×Q32
LCSG ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6370);