Finite Group Databasebeta

C2×#24923347 #36332825

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24923347

Splittings

SylowC167 ⋊ C2×#436

Subgroups

subgroupG/H
centerC22×C4C22×D167
commutatorC22×C167C23×C4
FrattiniC2×C4C23×D167
FittingC2×C4×D4×C167C2
socleC23×C167C22×C4
prime radicalC22×D4×C167C4
cosocleC2×C4×C167C24
hypercenterC2×C4×D4D167
hypocenterC167C2×#436
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

3376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 13197);