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#117×Dic67 #22562552

order8576
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic67

Splittings

SylowC67 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D67
commutatorC2×C67C22×C42
FrattiniC23C23×D67
FittingC2×#117×C67C2
socleC23×C67C24
hypercenterC2×#117D67
hypocenterC67C4×#117
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#30749272, #30749276, H(3,ℤ/4)×Dic67, …
maximal normal subgroup of#30749272, #30749276, H(3,ℤ/4)×Dic67, …
maximal quotient of#376×Dic67, C4×C22⋊C4×Dic67, C4×C4⋊C4×Dic67, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8576, 6853);