Finite Group Databasebeta

C2×#13093959 #15689168

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

Aliases

direct productC2×#13093959

Splittings

SylowC47 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D47
commutatorC4×C47C22×C4
FrattiniC2×C4C22×D47
FittingC2×M16×C47C2
socleC22×C47C4⋊C4
prime radicalC23×C47Q8
cosocleC2×C4×C47C23
hypercenterC2×M16D47
hypocenterC47C2×#108
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 594);