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C4×#88198 #13117404

order1664
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#88198

Splittings

SylowC13 ⋊ C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D13
commutatorC22×C13C23×C4
FrattiniC23C23×D13
FittingC2×C4×Q8×C13C2
socle, prime radical, cosocleC23×C13C24
hypercenterC2×C4×Q8D13
hypocenterC13C4×C4⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

Relationships

maximal subgroup of#15757566, #15757567, #15757569, …
maximal normal subgroup of#15757566, #15757567, #15757569, …
maximal quotient ofC4×#11718633, C4×#11718891, C4×#11718635, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 7078);