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C2×2−1+4×#64408 #34032701

order18688
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×#64408
unambiguous semidirect productD73⋊(C4×2−1+4)

Splittings

FittingC2×2−1+4×C73 ⋊ C4
SylowC73 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC22C24×#64408
commutatorC2×C73C25×C4
FrattiniC2C25×#64408
FittingC2×2−1+4×C73C4
socleC22×C73C24×C4
prime radicalC2×2−1+4×D73C2
cosocleC2×D73C26
hypercenterC2×2−1+4#64408
hypocenterC73C2×C4×2−1+4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1116285);