Finite Group Databasebeta

C2×#14270917 #16819182

order3712
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14270917

Splittings

SylowC29 ⋊ C2×#336

Subgroups

subgroupG/H
centerC23×C4C2×D29
commutatorC2×C29C2×C4×C8
FrattiniC22×C4C22×D29
FittingC23×C8×C29C2
socle, prime radicalC24×C29C2×C4
cosocleC22×C4×C29C23
hypercenterC23×C8D29
hypocenterC29C2×#336
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C23×C4 ◁ C23×C8

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 4200);