Finite Group Databasebeta

C22×Dic47⋊C4 #15689573

order3008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×Dic47⋊C4

Splittings

SylowC47 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D47
commutatorC2×C47C23×C4
FrattiniC22C23×D47
FittingC23×C4×C47C2
socle, prime radicalC24×C47C22
cosocleC22×C47C24
hypercenterC23×C4D47
hypocenterC47C22×C4⋊C4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3008

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 999);