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#117×Dic53 #20277058

order6784
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic53

Splittings

SylowC53 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D53
commutatorC2×C53C22×C42
FrattiniC23C23×D53
FittingC2×#117×C53C2
socleC23×C53C24
hypercenterC2×#117D53
hypocenterC53C4×#117
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#27277533, #27277537, H(3,ℤ/4)×Dic53, …
maximal normal subgroup of#27277533, #27277537, H(3,ℤ/4)×Dic53, …
maximal quotient of#376×Dic53, C4×C22⋊C4×Dic53, C4×C4⋊C4×Dic53, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6784, 6853);