Finite Group Databasebeta

C2×#13093943 #15689103

order3008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13093943

Splittings

SylowC47 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic47
commutatorC22×C47C22×C4
FrattiniC2×C4C22×D47
FittingC22×Q8×C47C2
socleC22×C47C22⋊C4
prime radicalC23×C47C2×C4
cosocleC2×C4×C47C23
hypercenterC22×Q8D47
hypocenterC47C2×#101
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 529);