Finite Group Databasebeta

C2×#24923391 #36333034

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

Aliases

direct productC2×#24923391

Splittings

SylowC167 ⋊ C2×#444

Subgroups

subgroupG/H
centerC2×C4D4×D167
commutatorC4×C167C23×C4
FrattiniC2×C4C23×D167
Fitting, prime radicalC2×#135×C167C2
socleC22×C167C4×D4
cosocleC2×C4×C167C24
hypercenterC2×#135D167
hypocenterC167C2×#444
LCSG ▷ C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5344

Conjugacy classes & character table

2368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 13406);