Finite Group Databasebeta

C2×#27189634 #39909224

order26176
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27189634

Splittings

SylowC409 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic409
commutatorC22×C409C22×C4
FrattiniC2×C4C22×D409
Fitting, prime radicalC22×D4×C409C2
socleC22×C409C22⋊C4
cosocleC2×C4×C409C23
hypercenterC22×D4D409
hypocenterC409C2×#100
LCSG ▷ C22×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6544

Conjugacy classes & character table

4102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 526);