Finite Group Databasebeta

C2×C22⋊Dic947 #44476202

order30304
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic947

Splittings

SylowC947 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D947
commutatorC2×C947C22×C4
FrattiniC22C22×D947
Fitting, prime radicalC24×C947C2
socleC23×C947C22
cosocleC22×C947C23
hypercenterC24D947
hypocenterC947C2×C22⋊C4
LCSG ▷ C2×C947 ▷ C947
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15152

Conjugacy classes & character table

7588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30304, 98);