Finite Group Databasebeta

← Prev (#30874263) Next (#30874265) →

C4⋊C4×Dic268 #30874264

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic268

Splittings

SylowC67 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C22×D268
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC8×C4⋊C4×C67C2
socle, prime radicalC23×C67C22×D4
cosocleC22×C4×C67C24
hypercenterC8×C4⋊C4D67
hypocenterC67C4⋊C4×Q16
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 188001);