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C8×#13093637 #26045844

order11936
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C4

Aliases

direct productC8×#13093637

Splittings

FittingC8×C373 ⋊ C4
derived, SylowC373 ⋊ C4×C8

Subgroups

subgroupG/H
center, hypercenterC8#13093637
commutator, hypocenterC373C4×C8
FrattiniC4C2×#13093637
FittingC8×C373C4
socleC2×C373C42
prime radicalC2×D373C2×C4
cosocleC4×D373C22
LCSG ▷ C373
UCSC1 ◁ C8

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

776 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC16×#13093637, #37560309, C2×C8×#13093637, …
maximal normal subgroup ofC16×#13093637, #37560309, C2×C8×#13093637, …
maximal quotient ofC8×#15688419, #15688419⋊C8, (C2×#13093637)⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 198);