Finite Group Databasebeta

C2×#23764974 #34318233

order20224
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#23764974

Splittings

SylowC79 ⋊ C2×#2102

Subgroups

subgroupG/H
centerC2×C4#14579148
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC2×#430×C79C2
socleC22×C79#400
prime radicalC24×C79#41
hypercenterC2×#430D79
hypocenterC79C2×#2102
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2528

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 199532);