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C4⋊C4×#63254 #17193634

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4⋊C4×#63254

Splittings

FittingD4×C4⋊C4×C17 ⋊ C2
SylowC17 ⋊ C4⋊C4×#41

Subgroups

subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingD4×C4⋊C4×C17C2
socle, cosocleC23×C17C25
prime radicalC22×#63254C22
hypercenterD4×C4⋊C4D17
hypocenterC17C4⋊C4×#41
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ D4×C4⋊C4

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328878);