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C4×#15668060 #26033464

order11392
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#15668060

Splittings

FittingC2×C4×Q8×C89 ⋊ C2
SylowC89 ⋊ C4×2−1+4

Subgroups

subgroupG/H
centerC2×C4C23×D89
commutatorC2×C89C24×C4
FrattiniC22C24×D89
FittingC2×C4×Q8×C89C2
socle, cosocleC22×C89C25
prime radicalC2×#15668060C2
hypercenterC2×C4×Q8D89
hypocenterC89C4×2−1+4
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

1492 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1828 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36445831, #36445834, #36520812, …
maximal normal subgroup of#36445831, #36445834, #36520812, …
maximal quotient ofC4×#19152079, C4×#19152080, C4×#19152074, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 17722);