Finite Group Databasebeta

C2×#23750500 #34060381

order19072
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#23750500

Splittings

SylowC149 ⋊ C2×#341

Subgroups

subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC4×C149C2×C42
FrattiniC2×C4C22×#10597010
FittingC2×M16×C149C4
socleC22×C149#95
prime radicalC23×D149Q8
cosocleC2×C4×D149C23
hypercenterC2×M16#10597010
hypocenterC149C2×#341
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4768

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 20200);