Finite Group Databasebeta

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C2×M16×Dic59 #21432503

order7552
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic59

Splittings

SylowC59 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D59
commutatorC2×C59C22×C42
FrattiniC2×C4C23×D59
FittingC22×M16×C59C2
socleC23×C59C22×C4
hypercenterC22×M16D59
hypocenterC59C2×C4×M16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic59, #338×Dic59, #339×Dic59, …
maximal normal subgroup ofH(3,ℤ/4)×Dic59, #338×Dic59, #339×Dic59, …
maximal quotient ofC2×M16×C59⋊C8, C2×#21422377, C2×#21422383, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7552, 12917);