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C4×2−1+4×D79 #35194874

order20224
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×2−1+4×D79

Splittings

FittingC4×2−1+4×C79 ⋊ C2
SylowC79 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC2×C4C24×D79
commutatorC2×C79C25×C4
FrattiniC22C25×D79
FittingC4×2−1+4×C79C2
socle, cosocleC22×C79C26
prime radicalC2×2−1+4×D79C2
hypercenterC4×2−1+4D79
hypocenterC79C2×C4×2−1+4
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

2788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1076173);