Finite Group Databasebeta

C2×#13093989 #15689587

order3008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13093989

Splittings

SylowC47 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D47
commutatorC2×C47C23×C4
FrattiniC22C23×D47
FittingC2×C4⋊C4×C47C2
socle, prime radicalC23×C47C23
cosocleC22×C47C24
hypercenterC2×C4⋊C4D47
hypocenterC47C2×C4×Q8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4⋊C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3008

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 1013);