Finite Group Databasebeta

C4×Dic1912 #44486408

order30592
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic1912

Splittings

SylowC239 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC2×C4D1912
commutatorC8×C239C22×C4
FrattiniC2×C8C22×D239
FittingC4×C16×C239C2
socle, prime radicalC22×C239C2×D8
cosocleC2×C8×C239C23
hypercenterC4×C16D239
hypocenterC239C4×Q32
LCSG ▷ C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

7660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6370);