Finite Group Databasebeta

C4×Dic2092 #45690301

order33472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic2092

Splittings

SylowC523 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4D2092
commutatorC4×C523C22×C4
FrattiniC2×C4C22×D523
FittingC4×C8×C523C2
socle, prime radicalC22×C523C2×D4
cosocleC2×C4×C523C23
hypercenterC4×C8D523
hypocenterC523C4×Q16
LCSG ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33472

Conjugacy classes & character table

8380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 645);