Finite Group Databasebeta

C2×#14556537 #17989014

order4672
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14556537

Splittings

SylowC73 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#11924013
commutator, cosocleC8×C73C23
FrattiniC8C22×D73
FittingC2×Q16×C73C2
socle, prime radicalC22×C73D8
hypercenterC2×Q16D73
hypocenterC73C2×Q32
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 976);