Finite Group Databasebeta

C2×#21418478 #28416858

order14912
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#21418478

Splittings

FittingC2×Q16×C233 ⋊ C2
SylowC233 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#16836579
commutator, cosocleC8×C233C23
FrattiniC8C22×D233
FittingC2×Q16×C233C2
socleC22×C233D8
prime radicalC2×D1864C2
hypercenterC2×Q16D233
hypocenterC233C2×SD32
LCSG ▷ C8×C233 ▷ C4×C233 ▷ C2×C233 ▷ C233
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

Conjugacy classes & character table

1646 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 972);