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#117×Dic59 #21426439

order7552
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic59

Splittings

SylowC59 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D59
commutatorC2×C59C22×C42
FrattiniC23C23×D59
FittingC2×#117×C59C2
socleC23×C59C24
hypercenterC2×#117D59
hypocenterC59C4×#117
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#117

752 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 of#28482130, #28482134, H(3,ℤ/4)×Dic59, …
maximal normal subgroup of#28482130, #28482134, H(3,ℤ/4)×Dic59, …
maximal quotient of#376×Dic59, C4×C22⋊C4×Dic59, C4×C4⋊C4×Dic59, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7552, 6853);