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C22×(C2×D83)⋊C4 #19128148

order5312
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D83)⋊C4

Splittings

FittingC23×C4×C83 ⋊ C2
SylowC83 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D83
commutatorC2×C83C23×C4
FrattiniC22C23×D83
FittingC23×C4×C83C2
socleC24×C83C22
hypercenterC23×C4D83
hypocenterC83C22×C22⋊C4
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#19127548, C2×C4×(C2×D83)⋊C4, #24909815, …
maximal normal subgroup ofC2×#19127548, C2×C4×(C2×D83)⋊C4, #24909815, …
maximal quotient ofC22×C83⋊#95, C2×C4×(C2×D83)⋊C4, C2×#19127556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5312, 996);