Finite Group Databasebeta

C4×Dic1592 #38770710

order25472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic1592

Splittings

SylowC199 ⋊ C4×Q32

Subgroups

subgroupG/H
centerC2×C4D1592
commutatorC8×C199C22×C4
FrattiniC2×C8C22×D199
FittingC4×C16×C199C2
socle, prime radicalC22×C199C2×D8
cosocleC2×C8×C199C23
hypercenterC4×C16D199
hypocenterC199C4×Q32
LCSG ▷ C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25472

Conjugacy classes & character table

6380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 6370);