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Q8×(C22⋊D79)⋊C4 #34448128

order20224
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×(C22⋊D79)⋊C4

Splittings

FittingQ8×C22⋊C4×C79 ⋊ C2
SylowC79 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingQ8×C22⋊C4×C79C2
socle, cosocleC23×C79C25
prime radicalC22×C22⋊D79C23
hypercenterQ8×C22⋊C4D79
hypocenterC79C4×D4×Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

3148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

2050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 329427);